What you’ll learn
Solve tangent/chord angle problems.
Key idea
The tangent-chord angle is half its intercepted arc; the 90-degree theorem concerns the contact radius.
Radius-tangent perpendicularity does not assign 90 degrees to every tangent-chord angle.
Worked example
Enter the exact value or ordered values in the format requested below.
The tangent at T and chord TA form the acute angle opening toward minor arc TA=170 degrees. Find that angle in degrees.
- Use the tangent-chord half-arc relation for the explicitly selected acute angle.
- Angle=170/2=85 degrees.
Answer: 85
Quick Check
Evaluate a worked attempt at solve tangent/chord angle problems, identify the first invalid step, and provide the correction.
Tangent at T and chord TA intercept minor arc TA=100 degrees. Step 1 says the tangent is perpendicular to radius OT. Step 2 says the tangent-chord angle toward that minor arc is 90 degrees. Locate and repair the first invalid step.